Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x+12=5
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Equation 1-x/2=x/3
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Equation x^2+x=12
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Equation x^4=(x-56)^2
- Express {x} in terms of y where:
- 18*x+19*y=7
- 8*x-13*y=-12
- 1*x+6*y=6
- -6*x+1*y=-5
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Identical expressions
- (two *x+ nineteen)*(two *x+ fourteen)-((twenty-seven -(two *x+ seventeen)^ three))/((((sqrt(- two *x- eighteen)^ two)+ four)))=(- two *x- seventeen)*(|x+ eight |)- twenty-five
- (2 multiply by x plus 19) multiply by (2 multiply by x plus 14) minus ((27 minus (2 multiply by x plus 17) cubed )) divide by (((( square root of ( minus 2 multiply by x minus 18) squared ) plus 4))) equally ( minus 2 multiply by x minus 17) multiply by ( module of x plus 8|) minus 25
- (two multiply by x plus nineteen) multiply by (two multiply by x plus fourteen) minus ((twenty minus seven minus (two multiply by x plus seventeen) to the power of three)) divide by (((( square root of ( minus two multiply by x minus eighteen) to the power of two) plus four))) equally ( minus two multiply by x minus seventeen) multiply by ( module of x plus eight |) minus twenty minus five
- (2*x+19)*(2*x+14)-((27-(2*x+17)^3))/((((√(-2*x-18)^2)+4)))=(-2*x-17)*(|x+8|)-25
- (2*x+19)*(2*x+14)-((27-(2*x+17)3))/((((sqrt(-2*x-18)2)+4)))=(-2*x-17)*(|x+8|)-25
- 2*x+19*2*x+14-27-2*x+173/sqrt-2*x-182+4=-2*x-17*|x+8|-25
- (2*x+19)*(2*x+14)-((27-(2*x+17)³))/((((sqrt(-2*x-18)²)+4)))=(-2*x-17)*(|x+8|)-25
- (2*x+19)*(2*x+14)-((27-(2*x+17) to the power of 3))/((((sqrt(-2*x-18) to the power of 2)+4)))=(-2*x-17)*(|x+8|)-25
- (2x+19)(2x+14)-((27-(2x+17)^3))/((((sqrt(-2x-18)^2)+4)))=(-2x-17)(|x+8|)-25
- (2x+19)(2x+14)-((27-(2x+17)3))/((((sqrt(-2x-18)2)+4)))=(-2x-17)(|x+8|)-25
- 2x+192x+14-27-2x+173/sqrt-2x-182+4=-2x-17|x+8|-25
- 2x+192x+14-27-2x+17^3/sqrt-2x-18^2+4=-2x-17|x+8|-25
- (2*x+19)*(2*x+14)-((27-(2*x+17)^3)) divide by ((((sqrt(-2*x-18)^2)+4)))=(-2*x-17)*(|x+8|)-25
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Similar expressions
- (2*x-19)*(2*x+14)-((27-(2*x+17)^3))/((((sqrt(-2*x-18)^2)+4)))=(-2*x-17)*(|x+8|)-25
- (2*x+19)*(2*x+14)-((27-(2*x+17)^3))/((((sqrt(-2*x+18)^2)+4)))=(-2*x-17)*(|x+8|)-25
- (2*x+19)*(2*x+14)-((27-(2*x+17)^3))/((((sqrt(-2*x-18)^2)+4)))=(-2*x-17)*(|x-8|)-25
- (2*x+19)*(2*x-14)-((27-(2*x+17)^3))/((((sqrt(-2*x-18)^2)+4)))=(-2*x-17)*(|x+8|)-25
- (2*x+19)*(2*x+14)-((27-(2*x+17)^3))/((((sqrt(2*x-18)^2)+4)))=(-2*x-17)*(|x+8|)-25
- (2x+19)*(2x+14)-((27-(2x+17)^3))/((((√(-2x-18)^2)+4)))=(-2x-17)*|x+8|-25
- (2*x+19)*(2*x+14)+((27-(2*x+17)^3))/((((sqrt(-2*x-18)^2)+4)))=(-2*x-17)*(|x+8|)-25
- (2*x+19)*(2*x+14)-((27-(2*x+17)^3))/((((sqrt(-2*x-18)^2)+4)))=(-2*x+17)*(|x+8|)-25
- (2*x+19)*(2*x+14)-((27-(2*x+17)^3))/((((sqrt(-2*x-18)^2)+4)))=(2*x-17)*(|x+8|)-25
- (2*x+19)*(2*x+14)-((27-(2*x-17)^3))/((((sqrt(-2*x-18)^2)+4)))=(-2*x-17)*(|x+8|)-25
- (2*x+19)*(2*x+14)-((27+(2*x+17)^3))/((((sqrt(-2*x-18)^2)+4)))=(-2*x-17)*(|x+8|)-25
- (2*x+19)*(2*x+14)-((27-(2*x+17)^3))/((((sqrt(-2*x-18)^2)-4)))=(-2*x-17)*(|x+8|)-25
- (2*x+19)*(2*x+14)-((27-(2*x+17)^3))/((((sqrt(-2*x-18)^2)+4)))=(-2*x-17)*(|x+8|)+25
(2*x+19)*(2*x+14)-((27-(2*x+17)^3))/((((sqrt(-2*x-18)^2)+4)))=(-2*x-17)*(|x+8|)-25 equation
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The solution
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3
27 - (2*x + 17)
(2*x + 19)*(2*x + 14) - ------------------ = (-2*x - 17)*|x + 8| - 25
2
___________
\/ -2*x - 18 + 4
$$- \frac{27 - \left(2 x + 17\right)^{3}}{\left(\sqrt{- 2 x - 18}\right)^{2} + 4} + \left(2 x + 14\right) \left(2 x + 19\right) = \left(- 2 x - 17\right) \left|{x + 8}\right| - 25$$
Detail solution
For every modulo expressions in the equation
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.
1.
$$x + 8 \geq 0$$
or
$$-8 \leq x \wedge x < \infty$$
we get the equation
$$- \frac{27 - \left(2 x + 17\right)^{3}}{- 2 x - 14} - \left(- 2 x - 17\right) \left(x + 8\right) + \left(2 x + 14\right) \left(2 x + 19\right) + 25 = 0$$
after simplifying we get
$$- \frac{27 - \left(2 x + 17\right)^{3}}{- 2 x - 14} - \left(- 2 x - 17\right) \left(x + 8\right) + \left(2 x + 14\right) \left(2 x + 19\right) + 25 = 0$$
the solution in this interval:
$$x_{1} = - \frac{13}{2}$$
$$x_{2} = -6$$
2.
$$x + 8 < 0$$
or
$$-\infty < x \wedge x < -8$$
we get the equation
$$- \frac{27 - \left(2 x + 17\right)^{3}}{- 2 x - 14} - \left(- 2 x - 17\right) \left(- x - 8\right) + \left(2 x + 14\right) \left(2 x + 19\right) + 25 = 0$$
after simplifying we get
$$- \frac{27 - \left(2 x + 17\right)^{3}}{- 2 x - 14} - \left(- 2 x - 17\right) \left(- x - 8\right) + \left(2 x + 14\right) \left(2 x + 19\right) + 25 = 0$$
the solution in this interval:
$$x_{3} = - \frac{41}{4} - \frac{\sqrt{129}}{4}$$
$$x_{4} = - \frac{41}{4} + \frac{\sqrt{129}}{4}$$
but x4 not in the inequality interval
The final answer:
$$x_{1} = - \frac{13}{2}$$
$$x_{2} = -6$$
$$x_{3} = - \frac{41}{4} - \frac{\sqrt{129}}{4}$$
allow cases, when this expressions ">=0" or "<0",
solve the resulting equation.
1.
$$x + 8 \geq 0$$
or
$$-8 \leq x \wedge x < \infty$$
we get the equation
$$- \frac{27 - \left(2 x + 17\right)^{3}}{- 2 x - 14} - \left(- 2 x - 17\right) \left(x + 8\right) + \left(2 x + 14\right) \left(2 x + 19\right) + 25 = 0$$
after simplifying we get
$$- \frac{27 - \left(2 x + 17\right)^{3}}{- 2 x - 14} - \left(- 2 x - 17\right) \left(x + 8\right) + \left(2 x + 14\right) \left(2 x + 19\right) + 25 = 0$$
the solution in this interval:
$$x_{1} = - \frac{13}{2}$$
$$x_{2} = -6$$
2.
$$x + 8 < 0$$
or
$$-\infty < x \wedge x < -8$$
we get the equation
$$- \frac{27 - \left(2 x + 17\right)^{3}}{- 2 x - 14} - \left(- 2 x - 17\right) \left(- x - 8\right) + \left(2 x + 14\right) \left(2 x + 19\right) + 25 = 0$$
after simplifying we get
$$- \frac{27 - \left(2 x + 17\right)^{3}}{- 2 x - 14} - \left(- 2 x - 17\right) \left(- x - 8\right) + \left(2 x + 14\right) \left(2 x + 19\right) + 25 = 0$$
the solution in this interval:
$$x_{3} = - \frac{41}{4} - \frac{\sqrt{129}}{4}$$
$$x_{4} = - \frac{41}{4} + \frac{\sqrt{129}}{4}$$
but x4 not in the inequality interval
The final answer:
$$x_{1} = - \frac{13}{2}$$
$$x_{2} = -6$$
$$x_{3} = - \frac{41}{4} - \frac{\sqrt{129}}{4}$$
Sum and product of roots
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sum
_____
41 \/ 129
-6 - 13/2 + - -- - -------
4 4
$$\left(- \frac{41}{4} - \frac{\sqrt{129}}{4}\right) + \left(- \frac{13}{2} - 6\right)$$
=
_____ 91 \/ 129 - -- - ------- 4 4
$$- \frac{91}{4} - \frac{\sqrt{129}}{4}$$
product
/ _____\ -6*(-13) | 41 \/ 129 | --------*|- -- - -------| 2 \ 4 4 /
$$- -39 \left(- \frac{41}{4} - \frac{\sqrt{129}}{4}\right)$$
=
_____ 1599 39*\/ 129 - ---- - ---------- 4 4
$$- \frac{1599}{4} - \frac{39 \sqrt{129}}{4}$$
-1599/4 - 39*sqrt(129)/4
Rapid solution
[src]
x1 = -13/2
$$x_{1} = - \frac{13}{2}$$
x2 = -6
$$x_{2} = -6$$
_____
41 \/ 129
x3 = - -- - -------
4 4
$$x_{3} = - \frac{41}{4} - \frac{\sqrt{129}}{4}$$
x3 = -41/4 - sqrt(129)/4